Figure 1

(Color online) Comparisons of numerical simulations and experiments for different arrays of gold nanoparticles. The different columns (from left to right) show shape of nanoparticles, the polarization of the incident light (indicated by the arrows), the linear transmission (solid) and reflection (dashed) spectra, theoretical SHG spectra (amplified 13 orders of magnitude), the relative strengths obtained by the theory, and the corresponding experiments (inside brackets). For all the structures, the polarization of the generated second-harmonic waves is along the $y$ direction. The illuminating fundamental-frequency wave has a wavelength around 1500 nm and amplitude of $2\times {10}^7\left(\text{V}/\text{m}\right)$. (a) The U-shaped particle corresponds to the experimental sample shown in Fig. (1a) of Ref. 34 [also at Fig. (1a) of Ref. 40] with lattice constant $a_x=a_y=305\text{nm}$. (b) The C-shaped particle corresponds to the experimental sample shown in Fig. (1c) of Ref. 34 [also at Fig. (1c) of Ref. 40] with $a_x=567.5\text{nm}$ and $a_y=590\text{nm}$. (c) The inverse-U-shaped particle corresponds to the experimental sample shown in Ref. 42, with $a_x=a_y=305\text{nm}$. (d) The T-shaped particle corresponds to the experimental sample shown in Fig. (2c) of Ref. 40, with $a_x=295\text{nm}$ and $a_y=465\text{nm}$. (e) The rectangle-shaped corresponds to the experimental sample shown in Fig. (2b) of Ref. 40. Here $a_x$ and $a_y$ are the lattice constants along the $x$ and $y$ directions, respectively. All nanoparticle dimensions shown are in nm.Reuse & Permissions

Figure 2

(Color online) The polarization state of the second-harmonic emission from an array of U-shaped particles illuminated with a $x$-polarized plane wave at the fundamental frequency. The second-harmonic signal is a function of the measuring angle (not the polarization of the incident field) $\theta$ ($\theta =0$ corresponds to the $x$ direction). The corresponding experiment measurement is shown in Fig. (2b) of Ref. 34.Reuse & Permissions

Figure 3

(Color online) Second-harmonic generation in noncentrosymmetric nanodimers with varying gaps. The configuration such as $YXX$ indicates $y$-polarized second-harmonic signal with $x$-polarized fundamental field. The two images show the unit cells as simulated containing two structures which were digitized from the scanning electron micrograph images of the experimental samples (Ref. 39). The corresponding experimental results are reported in Ref. 39 (Figs. 1, 3).Reuse & Permissions